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Normal subsystems of fusion systems
Author(s) -
Aschbacher Michael
Publication year - 2008
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdm057
Subject(s) - mathematics , context (archaeology) , homotopy , fusion , representation (politics) , systems theory , algebra over a field , modular design , pure mathematics , computer science , artificial intelligence , linguistics , programming language , paleontology , philosophy , politics , political science , law , biology
The notion of a fusion system was first defined and explored by Puig in the context of modular representation theory. Later, Broto, Levi, and Oliver significantly extended the theory of fusion systems as a tool in homotopy theory. In this paper we begin a program to establish a local theory of fusion systems similar to the local theory of finite groups. In particular, we define the notion of a normal subsystem of a saturated fusion system, and prove some basic results about normal subsystems and factor systems.